Heat Transfer Through a Plane Wall

  1. 1. The problem statement, all variables and given/known data
    Consider a large plane wall of thickness L = 0.4m, thermal conductivity k = 1.8W/(m*K), and surface area A = 30m2. The left side of the wall is maintained at a constant temperature of T1 = 90 C while the right side looses heat by convection to the surrounding air at Ts = 25 C with a heat transfer coefficient of h = 24 W(m2*K). Assuming constant thermal conductivity and no heat generation in the wall evaluate the rate of heat transfer through the wall.
    Answer: 7079 W

    My answer doesn't match the book's answer.

    2. Relevant equations
    [tex]\dot{Q}_{wall} = -kA\frac{dT(0)}{dx}[/tex]
    [tex]\frac{d^2T}{dx^2} = 0[/tex]
    [tex]T(0) = 90[/tex]
    [tex]-k\frac{dT(L)}{dx} = h[T(L) - Ts][/tex]

    3. The attempt at a solution

    Solving the differential equation and applying B.C.:
    [tex]T(x) = xC_1 + C_2[/tex]
    [tex]T(0) = C_2 = 90[/tex]
    [tex]-kC_1 = hLC_1+hC_2-25h][/tex]
    [tex]C_1 = -\frac{h(C_2-25)}{k+hL}[/tex]

    Plugging numbers in:
    [tex]C_2 = 90[/tex]
    [tex]C_1 = -136.8[/tex]
    [tex]T(x) = 90-136.8x[/tex]
    [tex]\dot{Q}_{wall} = -1.8*30*(-136.8) = 7,387 W[/tex]

    Did I make a mistake or is the book's answer wrong?
  2. jcsd
  3. rude man

    rude man 6,000
    Homework Helper
    Gold Member

    I used a somewhat different approach (underlying equations are of course the same) and got the same answer you did.

    I computed the thermal resitance of the wall as L/kA = 7.41e-3 K/W and the equivalent thermal resistance of the convection effect as 1/hA = 1.39e-3 K/W, giving total thermal resistance of 8.80e-3 K/W so dQ/dt = (90 - 25)/8.80e-3 = 7387W.

    Just curious - what is your textbook?
  4. Awesome thanks, I didn't want to waste any more time redoing this problem looking for a mistake, and my class is just starting the thermal resistance chapter so if I see more problems that have wrong answers I'll do them that way to check.

    We're using Heat and Mass Transfer Fundamentals & Applications 4th Ed by Cengel and Ghajar.
  5. arent we suppose to take temp. as kelvin here?
  6. rude man

    rude man 6,000
    Homework Helper
    Gold Member

    It's OK to interchange K and C as long as you're dealing with temperature differences.
  7. oh ure right. new to the subject, just trying to learn sorry :) btw I personally know professor cengel and i will inform him about this. I will let you know about it. if you suspect any other mistake in the book feel free to ask please.
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